Problem: Solve for $x$ and $y$ using substitution. ${2x-y = 5}$ ${y = -2x+3}$
Explanation: Since $y$ has already been solved for, substitute $-2x+3$ for $y$ in the first equation. ${2x - }{(-2x+3)}{= 5}$ Simplify and solve for $x$ $2x+2x - 3 = 5$ $4x-3 = 5$ $4x-3{+3} = 5{+3}$ $4x = 8$ $\dfrac{4x}{{4}} = \dfrac{8}{{4}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = -2x+3}\thinspace$ to find $y$ ${y = -2}{(2)}{ + 3}$ $y = -4 + 3$ $y = -1$ You can also plug ${x = 2}$ into $\thinspace {2x-y = 5}\thinspace$ and get the same answer for $y$ : ${2}{(2)}{ - y = 5}$ ${y = -1}$